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Markkanen has played extensively in various European professional leagues as well as the NHL. He was selected in the fifth round of the 2001 NHL Entry Draft, 133rd overall, by the Edmonton Oilers, as an over-aged entrant.

Markkanen won the first Stanley Cup game of his career in Game 3 of the Finals against the Carolina Hurricanes on June 10, 2006, a game in which his play was stellar, earning himself the first star of the game.

In Game 5 of the Final, Markkanen and the Oilers grabbed victory when Edmonton beat Carolina 4–3 in OT thanks to Fernando Pisani's short-handed breakaway goal. This earned Markkanen his second-ever NHL playoff victory. The win saw him face 24 shots on goal.

Game 6 of the final in Edmonton saw Markkanen stop all 16 Hurricane shots, which earned him his first career playoff shutout and respect from many sports analysts. This victory led the Oilers to game 7 of the Stanley Cup Finals, which was held in Raleigh, North Carolina on June 192006. Carolina went on to be victorious in Game 7. Markkanen gave up two goals and the Hurricanes later secured the win with an empty net goal late in the third period, defeating Edmonton 3–1 to win the Stanley Cup.

After the great season in Edmonton, Markkanen did not regain the same form in the following season and after the 2006–07 NHL season, Markkanen was out of contract.

Markkanen was contracted by Finnish top-runners Jokerit, who replaced Scott Langkow with Markkanen. Markkanen's move was a bit controversial because he owns a part of SaiPa, which also plays in the Finnish SM-liiga with Jokerit.

Markkanen played the regular season well, placing on the top goalkeepers in the league. Markkanen however sustained a heavy injury during his first playoff game and missed the remainder of the playoffs.